Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-9y &= 6 \\ -6x-6y &= 3\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = 6y+3$ Divide both sides by $-6$ to isolate $x$ $x = {-y - \dfrac{1}{2}}$ Substitute this expression for $x$ in the first equation. $-5({-y - \dfrac{1}{2}}) - 9y = 6$ $5y + \dfrac{5}{2} - 9y = 6$ Simplify by combining terms, then solve for $y$ $-4y + \dfrac{5}{2} = 6$ $-4y = \dfrac{7}{2}$ $y = -\dfrac{7}{8}$ Substitute $-\dfrac{7}{8}$ for $y$ in the top equation. $-5x-9( -\dfrac{7}{8}) = 6$ $-5x+\dfrac{63}{8} = 6$ $-5x = -\dfrac{15}{8}$ $x = \dfrac{3}{8}$ The solution is $\enspace x = \dfrac{3}{8}, \enspace y = -\dfrac{7}{8}$.